Squeezed states of a particle in magnetic field

For a charged particle in a homogeneous magnetic field, we construct stationary squeezed states which are eigenfunctions of the Hamiltonian and the non-Hermitian operator % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0df9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lqpe0x% c9q8qqaqFn0dXdir-xcvk9pIe9q8qqaq-xir-f0-yqaqVeLsFr0-vr% 0-vr0dc8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGybGbaK% aadaWgaaWcbaGaeuOPdyeabeaakiabg2da9iqadIfagaqcaiGacoga% caGGVbGaai4CaiabfA6agjabgUcaRiqadMfagaqcaiGacohacaGGPb% GaaiOBaiabfA6agbaa!4894! $$\hat X_\Phi = \hat X\cos \Phi + \hat Y\sin \Phi $$ , % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0df9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lqpe0x% c9q8qqaqFn0dXdir-xcvk9pIe9q8qqaq-xir-f0-yqaqVeLsFr0-vr% 0-vr0dc8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaceWGybGbaK% aaaaa!3A82! $$\hat X$$ and Ŷ being the coordinates of the Larmor circle center and Φ is a complex parameter. In the family of the squeezed states, the quantum uncertainty in the Larmor circle position is minimal. The wave functions of the squeezed states in the coordinate representation are found and their properties are discussed. Besides, for arbitrary gauge of the vector potential we derive the symmetry operators of translations and rotations.

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